Categorical Landstad duality for actions S. KaliszewskiJohn Quigg 46L5546M1518A25full crossed productmaximal coactionLandstad dualitycategory equivalencecomma category We show that the category $\mathcal{A}(G)$ of actions of a locally compact group $G$ on $C^{*}$-algebras (with equivariant nondegenerate $*$-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of $G$ under the comultiplication $(C^{*}(G),\delta_G)$; and also that $\mathcal{A}(G)$ is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those $C^{*}$-algebras which are isomorphic to crossed products by $G$ as precisely those which form part of an object in the appropriate comma category. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3485 10.1512/iumj.2009.58.3485 en Indiana Univ. Math. J. 58 (2009) 415 - 442 state-of-the-art mathematics http://iumj.org/access/